Elements of Metric Spaces
Author: Manabendra Nath Mukherjee
Publisher: Academic Publishers
Published: 2010
Total Pages: 216
ISBN-13: 9788189781989
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Metric Spaces
Author: Mícheál O'Searcoid
Publisher: Springer
Published: 2009-10-12
Total Pages: 304
ISBN-13: 9781848004948
DOWNLOAD EBOOKThe abstract concepts of metric spaces are often perceived as difficult. This book offers a unique approach to the subject which gives readers the advantage of a new perspective on ideas familiar from the analysis of a real line. Rather than passing quickly from the definition of a metric to the more abstract concepts of convergence and continuity, the author takes the concrete notion of distance as far as possible, illustrating the text with examples and naturally arising questions. Attention to detail at this stage is designed to prepare the reader to understand the more abstract ideas with relative ease.
Metric Spaces
Author: Mícheál O'Searcoid
Publisher: Springer Science & Business Media
Published: 2006-12-26
Total Pages: 318
ISBN-13: 1846286271
DOWNLOAD EBOOKThe abstract concepts of metric spaces are often perceived as difficult. This book offers a unique approach to the subject which gives readers the advantage of a new perspective on ideas familiar from the analysis of a real line. Rather than passing quickly from the definition of a metric to the more abstract concepts of convergence and continuity, the author takes the concrete notion of distance as far as possible, illustrating the text with examples and naturally arising questions. Attention to detail at this stage is designed to prepare the reader to understand the more abstract ideas with relative ease.
Metric Spaces
Author: Satish Shirali
Publisher: Springer Science & Business Media
Published: 2006
Total Pages: 238
ISBN-13: 9781852339227
DOWNLOAD EBOOKOne of the first books to be dedicated specifically to metric spaces Full of worked examples, to get complex ideas across more easily
Topology of Metric Spaces
Author: S. Kumaresan
Publisher: Alpha Science Int'l Ltd.
Published: 2005
Total Pages: 172
ISBN-13: 9781842652503
DOWNLOAD EBOOK"Topology of Metric Spaces gives a very streamlined development of a course in metric space topology emphasizing only the most useful concepts, concrete spaces and geometric ideas to encourage geometric thinking, to treat this as a preparatory ground for a general topology course, to use this course as a surrogate for real analysis and to help the students gain some perspective of modern analysis." "Eminently suitable for self-study, this book may also be used as a supplementary text for courses in general (or point-set) topology so that students will acquire a lot of concrete examples of spaces and maps."--BOOK JACKET.
Set Theory and Metric Spaces
Author: Irving Kaplansky
Publisher: American Mathematical Society
Published: 2020-09-10
Total Pages: 140
ISBN-13: 1470463849
DOWNLOAD EBOOKThis is a book that could profitably be read by many graduate students or by seniors in strong major programs … has a number of good features. There are many informal comments scattered between the formal development of theorems and these are done in a light and pleasant style. … There is a complete proof of the equivalence of the axiom of choice, Zorn's Lemma, and well-ordering, as well as a discussion of the use of these concepts. There is also an interesting discussion of the continuum problem … The presentation of metric spaces before topological spaces … should be welcomed by most students, since metric spaces are much closer to the ideas of Euclidean spaces with which they are already familiar. —Canadian Mathematical Bulletin Kaplansky has a well-deserved reputation for his expository talents. The selection of topics is excellent. — Lance Small, UC San Diego This book is based on notes from a course on set theory and metric spaces taught by Edwin Spanier, and also incorporates with his permission numerous exercises from those notes. The volume includes an Appendix that helps bridge the gap between metric and topological spaces, a Selected Bibliography, and an Index.
Introduction to Metric and Topological Spaces
Author: Wilson A Sutherland
Publisher: Oxford University Press
Published: 2009-06-18
Total Pages: 219
ISBN-13: 0191568309
DOWNLOAD EBOOKOne of the ways in which topology has influenced other branches of mathematics in the past few decades is by putting the study of continuity and convergence into a general setting. This new edition of Wilson Sutherland's classic text introduces metric and topological spaces by describing some of that influence. The aim is to move gradually from familiar real analysis to abstract topological spaces, using metric spaces as a bridge between the two. The language of metric and topological spaces is established with continuity as the motivating concept. Several concepts are introduced, first in metric spaces and then repeated for topological spaces, to help convey familiarity. The discussion develops to cover connectedness, compactness and completeness, a trio widely used in the rest of mathematics. Topology also has a more geometric aspect which is familiar in popular expositions of the subject as `rubber-sheet geometry', with pictures of Möbius bands, doughnuts, Klein bottles and the like; this geometric aspect is illustrated by describing some standard surfaces, and it is shown how all this fits into the same story as the more analytic developments. The book is primarily aimed at second- or third-year mathematics students. There are numerous exercises, many of the more challenging ones accompanied by hints, as well as a companion website, with further explanations and examples as well as material supplementary to that in the book.
Lipschitz Algebras
Author: Nik Weaver
Publisher: World Scientific
Published: 1999
Total Pages: 242
ISBN-13: 9789810238735
DOWNLOAD EBOOKThe Lipschitz algebras Lp(M), for M a complete metric space, are quite analogous to the spaces C(omega) and Linfinity(X), for omega a compact Hausdorff space and X a sigma-finite measure space. Although the Lipschitz algebras have not been studied as thoroughly as these better-known cousins, it is becoming increasingly clear that they play a fundamental role in functional analysis, and are also useful in many applications, especially in the direction of metric geometry. This book gives a comprehensive treatment of (what is currently known about) the beautiful theory of these algebras.
Metric Spaces
Author: E. T. Copson
Publisher: CUP Archive
Published: 1988-02-11
Total Pages: 156
ISBN-13: 9780521357326
DOWNLOAD EBOOKProfessor Copson's book provides a more leisurely treatment of metric spaces than is found in books on functional analysis.
Elements of Point Set Topology
Author: John D. Baum
Publisher: Courier Corporation
Published: 1991-01-01
Total Pages: 164
ISBN-13: 0486668266
DOWNLOAD EBOOKTopology continues to be a topic of prime importance in contemporary mathematics, but until the publication of this book there were few if any introductions to topology for undergraduates. This book remedied that need by offering a carefully thought-out, graduated approach to point set topology at the undergraduate level. To make the book as accessible as possible, the author approaches topology from a geometric and axiomatic standpoint; geometric, because most students come to the subject with a good deal of geometry behind them, enabling them to use their geometric intuition; axiomatic, because it parallels the student's experience with modern algebra, and keeps the book in harmony with current trends in mathematics. After a discussion of such preliminary topics as the algebra of sets, Euler-Venn diagrams and infinite sets, the author takes up basic definitions and theorems regarding topological spaces (Chapter 1). The second chapter deals with continuous functions (mappings) and homeomorphisms, followed by two chapters on special types of topological spaces (varieties of compactness and varieties of connectedness). Chapter 5 covers metric spaces. Since basic point set topology serves as a foundation not only for functional analysis but also for more advanced work in point set topology and algebraic topology, the author has included topics aimed at students with interests other than analysis. Moreover, Dr. Baum has supplied quite detailed proofs in the beginning to help students approaching this type of axiomatic mathematics for the first time. Similarly, in the first part of the book problems are elementary, but they become progressively more difficult toward the end of the book. References have been supplied to suggest further reading to the interested student.
